www.liveperson.com is the premier solution, just for a benchmark. There are others out there.
For the totally free end of the spectrum...(II'll ask some developers who use open source all the time to see if they like anything better than AJAX.)
But check out AJAX, it's pretty popular (and free):
http://sourceforge.net/projects/ajax-chat/AJAX Chat is a fully customizable web chat implemented in JavaScript, PHP and MySQL which integrates nicely with common forum systems like phpBB, MyBB, PunBB, SMF and vBulletin. A Flash and Ruby based socket connection can be used to boost performance.